First of all, see this: Parthian Empire - History and Coins of Ancient Parthia
This is a very good recource about the Parthian history and archaeology which focuses almost exclusively on Parthian numismatics, because of the fact that Parthian coins are the only feasible method of reconstructing the Parthian dynastic history and validating Roman accounts.

Regarding your question I should say that Parthians for a long time regarded themselves as the successors of Alexander and patrons of the Greek culture. On many of their coins they frequently use the title "philellēnos" which seems to have been at least a socially obligatory thing for the legitimacy of the Arsacid rule.

Just like the Bactrian Kings, the language of the common subjects finally became their court language and this was when a shift to the Parthian language happened, which was rather early. By 200 AD, coins with Aramaic inscriptions (in Parthian language) start to appear within their kingdom. Of course the spoken language was never Greek, it was at first a variety of the Saka language and after that the Parthian vernacular, but we can assume that during a large part of the Parthian era Greek was used to write down records and probably histories in the Parthian court.

Regarding your question I should say that Parthians for a long time regarded themselves as the successors of Alexander and patrons of the Greek culture. On many of their coins they frequently use the title "philellēnos" which seems to have been at least a socially obligatory thing for the legitimacy of the Arsacid rule.

Just like the Bactrian Kings, the language of the common subjects finally became their court language and this was when a shift to the Parthian language happened, which was rather early. By 200 AD, coins with Aramaic inscriptions (in Parthian language) start to appear within their kingdom. Of course the spoken language was never Greek, it was at first a variety of the Saka language and after that the Parthian vernacular, but we can assume that during a large part of the Parthian era Greek was used to write down records and probably histories in the Parthian court.